Effects of aspect ratio on rolling and twisting foils

Abstract

Flapping flight and swimming are increasingly studied both due to their intrinsic scientific richness and their applicability to novel robotic systems. Strip theory is often applied to flapping wings, but such modeling is only rigorously applicable in the limit of infinite aspect ratio (A) where the geometry and kinematics are effectively uniform. This work compares the flow features and forces of strip theory and three dimensional flapping foils, maintaining similitude in the rolling and twisting kinematics while varying the foil A. We find the key influence of finite A and spanwise varying kinematics is the generation of a time-periodic spanwise flow which stabilizes the vortex structures and enhances the dynamics at the foil root. An aspect-ratio correction for flapping foils is developed analogous to Prandtl finite wing theory, enabling future use of strip theory in analysis and design of finite aspect ratio flapping foils.

Fin sweep angle does not determine flapping propulsive performance

“…The pivot point of pitch and twist is at the leading edge of the root section. The roll motion is simply rotation about the inline axis, and the amplitude is set to achieve the same amplitude A at l * similarly to maximum twist as described in [ 30 ].…”

“…The pivot point of pitch and twist is at the leading edge of the root section. The roll motion is simply rotation about the inline axis, and the amplitude is set to achieve the same amplitude A at l* similarly to maximum twist as described in [30]. The correlation data in figure 5d use the Pearson coefficient of correlation between two continuous sets of data, and the correlation ratio between a category set and a continuous dataset, defined as ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi P…”

“…This is caused by their lower CnormalPow¯ compared to engineering-inspired configurations. In addition, the penguin-like flipper case has a high ≈40% efficiency which is achievable because the long span and large twist amplitude combine to achieve a similar maximum angle of attack along the span [30]. All types of motion with lower amplitude (engineering-inspired) give efficiencies between 4 and 20% with pure heave giving lower efficiencies because of higher CnormalPow¯.…”

Fin sweep angle does not determine flapping propulsive performance

“…The pivot point of pitch and twist is at the leading edge of the root section. The roll motion is simply rotation about the inline axis, and the amplitude is set to achieve the same amplitude A at l * similarly to maximum twist as described in (30). The correlation data in Fig.…”

“…This is caused by their lower compared to engineering-inspired configurations. In addition, the penguin-like flipper case has a high ≈ 40% efficiency which is achievable because the long span and large twist amplitude combine to achieve a similar maximum angle of attack along the span (30). All types of motion with lower amplitude (engineering-inspired) give efficiencies between 4%-20% with pure heave giving lower efficiencies because of higher .…”